So can I just set it up as a matrix with u as my solution set?In other words, do there exist numbers, a, b, and c, such that
a+2b+ 7c= -1
-2a+ 5b+ 19c= -13
3a+ 4b+ 17c= -3
2a- 2c= 6
Solve any three of those equations then see if those values of a, b, and c make the remaining equation true.
You are supposed to find the values of a, b and c. If there are no values that fulfill the system of equations then the vector u doesn't belong to the subspace generated by the vi's. You can try to solve even by simple substitution. What x are you talking about?I set up a matrix and ended up with my bottom row showing 0=0. Does this make a difference if I can still find a solution for every x? At first I thought it would mean the vector does not fit, but now I see it just means that not all vectors will fit - but this one still can.
I set up a matrix:You are supposed to find the values of a, b and c. If there are no values that fulfill the system of equations then the vector u doesn't belong to the subspace generated by the vi's. You can try to solve even by simple substitution. What x are you talking about?